You're looking at Less Wrong's discussion board. This includes all posts, including those that haven't been promoted to the front page yet. For more information, see About Less Wrong.

shokwave comments on Syntacticism - Less Wrong Discussion

-3 Post author: ec429 23 September 2011 06:49AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (62)

You are viewing a single comment's thread.

Comment author: shokwave 23 September 2011 08:28:35AM 2 points [-]

But how do we know that □S ⇔ there is a proof of S in PA? Only by applying some meta-theory. And how do we know that statements reached in the meta-theory of the form "thus-and-such is true of PA" are true of PA? Only by applying a meta-meta-theory. There is no a-priori justification for the claim that "A formal system is in principle capable of talking about other formal systems", which claim is used by the proof that PA can talk about itself.

I am not sure how relevant it is, but this put me in the mind of what the tortoise said to achilles.